Finite Group DatabasebetaFinite Group Databasebeta| order | 11590 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D61⋊C5 |
| unambiguous semidirect product | D61⋊(C5×C19) |
| unambiguous semidirect product | (C61⋊C5)⋊(C2×C19) |
| unambiguous semidirect product | (C19×D61)⋊C5 |
| Fitting, socle, Hall | C19×C61 ⋊ C2×C5 |
| derived, Sylow | C61 ⋊ C2×C5×C19 |
| Hall | C19×C61⋊C5 ⋊ C2 |
| Hall | C19×D61 ⋊ C5 |
| Hall | C61⋊C5 ⋊ C2×C19 |
| Hall | D61 ⋊ C5×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D61⋊C5 |
| commutator, cosocle, hypocenter | C61 | C2×C5×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C61 | C2×C5 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
304 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#6923⋊C5, C19⋊(#6923⋊C5), D19×D61⋊C5, … |
| maximal normal subgroup of | C19×#6923⋊C5, C19⋊(#6923⋊C5), D19×D61⋊C5, … |
| maximal quotient of | C19×Dic61⋊C5, C2×C19×D61⋊C5, C3×C19×D61⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11590, 10);